Katerina D. Papoulia

Visco-hyperelastic model for filled rubbers used in vibration isolation

The short time and cyclic behavior of filled rubbers used in vibration isolation in the frequency range 10{sup {minus}2} to 10{sup 2} rad/s is examined. A form of the free-energy function consistent with the assumption of an additive stress decomposition is employed. A constitutive law for the inelastic part of the stress is provided, in the form of an integro-differential equation, which involves the fractional order derivative of the internal variable. It is assumed that the volumetric response of the material is elastic. The elasticity of rubber is modeled following classical models (e.g., Rivlin, Ogden), extended to include compressibility. Step-by-step integration of the constitutive law is performed. Simple shear experiments are used to assess the capability of the model to capture essential response characteristics, such as stiffness reduction under cyclic loading of increasing amplitude and the variation of dissipated energy with amplitude and frequency.

A transfer matrix approach to free vibrations of coupled shear walls

Abstract A conceptually simple and computationally efficient numerical model, based on the transfer matrix technique, is proposed for the prediction of the elastic behaviour of coupled shear walls. The model developed allows for: variation of geometric and material properties with the height; shear as well as axial deformation of both walls and beams; a certain degree of rigidity at their joints; and subsidence as well as elastic movement of the foundations. The method is numerically implemented and applied to the evaluation of natural frequencies and modes of free vibrations of the structure. Good agreement of its predictions with experimental results confirms its accuracy and efficiency. Further comparisons with previously obtained numerical results lead to an assessment of the effect of shear deformation of the walls on the higher frequencies and demonstrate the capacity of the method to yield all types of vibrational modes within a predefined frequency range. The paper also assesses the effect of elastic foundation properties on the lower natural frequencies.

Effective conductivity by a probability-based local method

A local method is developed for estimating the effective conductivity for materials with varying deterministic or random conductivity on domains with mixed boundary conditions. The effective conductivity is the conductivity of a virtual homogeneous material which behaves globally as the original heterogeneous material. It is shown that the effective conductivity can be calculated from the values of the potential at a relatively small number of points in the specimen. A method is developed for calculating the potential at an arbitrary point in the specimen directly, rather than extracting its value from a field solution. The method is based on some technical concepts related to properties of diffusion processes and an extension of Ito’s formula for continuous semimartingales to the case of reflected diffusion processes. However, the application of the method is intuitive and uses elementary Monte Carlo simulation algorithms. The paper presents essential facts proving the validity of the proposed method and...

An Algorithm for Two-Dimensional Mesh Generation Based on the Pinwheel Tiling

We propose a new two-dimensional meshing algorithm called PINW able to generate meshes that accurately approximate the distance between any two domain points by paths composed only of cell edges. This technique is based on an extension of pinwheel tilings proposed by Radin and Conway (see [C. Radin, Ann.of Math. (2), 139 (1994), pp. 661-702]). We prove that the algorithm produces triangles of bounded aspect ratio. This kind of mesh would be useful in cohesive interface finite element modeling when the crack propagation path is an outcome of a simulation process.

Mixed and selective reduced integration procedures in large strain hyperelastic analysis of nearly incompressible solids

We compare a mixed method and a displacement method with selective reduced integration for the finite element analysis of finite, nearly incompressible, hyperelasticity. The Simo-Taylor three-field variational formulation is extended to a general description which includes volumetric-deviatoric coupling and can readily be specialized to particular cases, such as the strain energy functions due to Rivlin or Ogden. The displacement formulation is obtained as a special case. Emphasis is placed on the treatment of incompressibility and the avoidance of volumetric locking. Classical incompressible strain energy functions, extended to include the effect of compressibility at the nearly incompressible limit, result in a penalty type algorithm for the imposition of near incompressibility. This is accomplished through the decomposition of strain into distortional and volumetric components. Shear locking is prevented through the use of higher order elements. All integrals are evaluated in the current configuration. The two methods have been implemented into the finite element code MSC/NASTRAN i . It is shown that the methods,

Buckling Analysis of Delaminated and Stitched Composite Plate System Under Hygrothermal Pressure

In this study, we develop a model for buckling of a partially delaminated composite plate with transverse stitching to resist out of plane deformations. The model applies to carbon fiber/polyimide matrix composites rapidly heated to around 370 °C, where it is known that steam-induced delamination (the popcorn effect) becomes an issue as the pressures generated approach the tensile strength of the matrix. Thus, a key element is the incorporation of this hygrothermal pressure within the formulation. This complex composite structure is modeled as two adhesively connected, specially orthotropic, rectangular plates, and the delaminations with internal vapor pressure are considered as holes in the adhesive layer. The intact regions of the adhesive layer and the stitches are modeled by continuous and discrete linear mechanical springs, respectively. The energy contributions of each component in the system are expressed in terms of out-of-plane displacements. The boundary conditions are that the system is simply supported along all edges so as to permit a Fourier sine series to approximate the transverse displacements. Application of the energy minimization approach gives a system of algebraic equations to determine the unknown weighting coefficients of the functions describing the transverse deflections of each plate layer. Deformed shapes of the system under axial compressive loads are obtained for different hygrothermally induced pressure conditions so as to show that the model works well. Parametric studies on critical buckling loads are performed for a few stitch and delamination configurations. It is found that stitching through delaminated areas can increase critical buckling loads and alter the sequence of corresponding mode shapes.

Non-differentiable energy minimization for cohesive fracture

An energy minimization approach to initially rigid cohesive fracture is proposed, whose key feature is a term for the energy stored in the interfaces that is nondifferentiable at the origin. A consequence of this formulation is that there is no need to define an activation criterion as a separate entity from the traction-displacement relationship itself. Instead, activation happens automatically when the load reaches a critical level because the minimizer of the potential no longer occurs at the 0-displacement level. Thus, the activation computation necessary in previous initially rigid formulations is now replaced by the computation of a minimizer of a nondifferentiable objective function. This immediately makes the method more amenable to implicit time stepping, since the activation criterion no longer interacts with the nonlinear solver for the next time step. A novel extension of the functional to the dynamic case is presented. The optimization problem is solved by a continuation (homotopy) method used in conjunction with an augmented Lagrangian and a trust region minimization algorithm to find the minimal energy configuration. Because the approach eliminates the need for an activation criterion, the algorithm sidesteps the complexities of time-discontinuity and traction-locking previously observed in relation to initially rigid models.

Pinwheel Meshes and Branching of Cohesive Cracks

We consider the use of cohesive interface models in a dynamic finite element setting to simulate crack branching under mode-I loading conditions as performed in an experiment by Sharon et al. [1] (Figure 1.)